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# Installation
## Dependencies
Schroedinger was build and tested using the following dependency list. Any
deviation may result in Schroedinger not working properly
- python 3.12+
- matplotlib 3.8.2
- numpy 2.0.0
- scipy 1.12.0
- pytest (optional, tests)
- build (optional, wheel creation)
- sphinx 5.1.1 (optional, documentation)
- sphix book theme (optional, documentation)
## Compile
To compile schroedinger and generate a wheel package in the `dist` folder run
python -m build -w
## Documentation
Documentation is stored in the `docs` folder and can be generated by running
cd docs
make html
# schrodinger\_solve
Solves the one-dimensional, time independent Schroedinger's equation for a given
system and generates files with the energies, potential, wave functions and
expectation value of the position of the particles. schrodinger\_solve takes a
file describing the parameters to use and the potential (see below for file
format).
## Usage
```text
schrodinger_solve [-h] [-o OUTPUT_DIR] filename
```
## Options
```text
positional arguments:
filename File describing the system to solve
options:
-h, --help show this help message and exit
-o OUTPUT_DIR, --output-dir OUTPUT_DIR
Output directory for the results
```
## Input file format
The input file format consist of a five line header followed by a csv style, two
column table describing the potential. Lines in the header that specify multiple
parameters are separated by whitespace characters (tab or space). Parameters
must be given in a fixed order. Comments discard the rest of the line and
may be added with a `#` character. An empty line is discarded and the next
non-empty line specifies the next parameter. A concrete example is given below.
```text
<mass>
<x-min> <x-max> <n-points>
<first-eigenvalue> <last-eigenvalue>
<interpolation-type>
<n>
<x1> <y1>
<x2> <y2>
...
<xn> <yn>
```
- mass: (real) Mass of the particle
- x-min, x-max: (real) Solution interval
- n-points: (integer) Number of points in the discretization of the solution
interval
- first-eigenvalue, last-eigenvalue: (integer) Interval of energy eigenvalues to
generate
Further examples can be found in the subfolders inside `test`
# schrodinger\_plot
Plots the solutions of schrodinger\_solve. Visualises the given potential
together with the eigenstates and the probability density. Also plots the
standard deviation of each energy level.
Solutions of schrodinger_solve must be in a directory together for
schrodinger\_plot to visualise them. Solution files must keep names given by
schrodinger\_solve.
The plot generated by schrodinger_plot can be altered with different scale and
axis limits to better visualize the solution. If no custom scale or limits are
given schrodinger\_solve will limit the plot by the limits of the potential as
well as the energies of the solution for a better initial result.
## Usage
```text
schrodinger_plot.py [-h] [-s SOLUTION_DIR] [-o OUTPUT_DIR] [--show SHOW] [-e EXPORT] [--scale SCALE] [-x XLIM] [-y1 ENERGY_LIM] [-y2 UNCERTAINTY_LIM]
```
## Options
```text
-h, --help show a help message
-s SOLUTION_DIR --solution_dir
the path of the solution directory (default: None)
-o OUTPUT_DIR --output_dir
the path where the pdf should be saved (default: None)
--show SHOW Boolean, if True the plot is shown directly (default:
True)
-e EXPORT --export
Boolean, if True the plot is exported as a pdf
(default: True)
--scale SCALE Float, scales the wave functions (default: 1.0)
-x XLIM --xlim Limit of the x-axis of the left plot. None or
tuple[float, float] of shape (x_min, x_max)(default:
None)
-y1 ENERGY_LIM --energy_lim
Limit of the y-axis of the left plot. None or
tuple[float, float] of shape (y_min, y_max)(default:
None)
-y2 UNCERTAINTY_LIM --uncertainty_lim
Limit of the y-axis of the right plot. None or
tuple[float, float] of shape (y_min, y_max)(default:
None)
```
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